Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 58, Issue 2, Pages 1069-1079Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2011.2168942
Keywords
Alternative duals; finite frames; harmonic frames; oversampling; quantization; Sigma-Delta
Funding
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0902720] Funding Source: National Science Foundation
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In this note, we show that by quantizing the N-dimensional frame coefficients of signals in R-d using rth-order Sigma-Delta quantization schemes, it is possible to achieve root-exponential accuracy in the oversampling rate lambda := N/d. In particular, we construct a family of finite frames tailored specifically for coarse Sigma-Delta quantization that admit themselves as both canonical duals and Sobolev duals. Our construction allows for error guarantees that behave as e(-c root lambda), where under a mild restriction on the oversampling rate, the constants are absolute. Moreover, we show that harmonic frames can be used to achieve the same guarantees, but with the constants now depending on d.
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